scipy.linalg.

hankel#

scipy.linalg.hankel(c, r=None)[source]#

Construct a Hankel matrix.

The Hankel matrix has constant anti-diagonals, with c as its first column and r as its last row. If the first element of r differs from the last element of c, the first element of r is replaced by the last element of c to ensure that anti-diagonals remain constant. If r is not given, then r = zeros_like(c) is assumed.

Parameters:

carray_like: First column of the matrix. Whatever the actual shape of c, it will be converted to a 1-D array.
rarray_like, optional: Last row of the matrix. If None, r = zeros_like(c) is assumed. r[0] is ignored; the last row of the returned matrix is [c[-1], r[1:]]. Whatever the actual shape of r, it will be converted to a 1-D array.

Returns:

A(len(c), len(r)) ndarray: The Hankel matrix. Dtype is the same as (c[0] + r[0]).dtype.

See also

toeplitz: Toeplitz matrix
circulant: circulant matrix

Examples

>>> from scipy.linalg import hankel
>>> hankel([1, 17, 99])
array([[ 1, 17, 99],
       [17, 99,  0],
       [99,  0,  0]])
>>> hankel([1,2,3,4], [4,7,7,8,9])
array([[1, 2, 3, 4, 7],
       [2, 3, 4, 7, 7],
       [3, 4, 7, 7, 8],
       [4, 7, 7, 8, 9]])